相互作用粒子系统 内容简介
my intention is that this book serve as a reference work on interacting particle systems， and that it be used as the basis for an advanced graduate course on this subject. the book should be of interest not only to mathematicians， but also to workers in related areas such as mathematical physics and mathematical biology. the prerequisites for reading it are solid one-year graduate courses in analysis and probability theory， at the level of royden （1968） and chung （1974）， respectively. material which is usually covered in these courses will be used without comment. in addition， a familiarity with a number of other types of stochastic processes will be helpful. however， references will be given when results from specialized parts of probability theory are used. no particular knowledge of statistical mechanics or mathematical biology is assumed. while this is the first book-length treatment of the subject of interacting particle systems， a number of surveys of parts of the field have appeared in recent years. among these are spitzer （1974a）， holley （1974a）， sullivan （1975b）， liggett （1977b）， stroock （1978）， griffeath （1979a， 1981）， and durrett （1981）. these can serve as useful comolements to the oresent work.
相互作用粒子系统 目录
frequently used notation
introduction
chapter ⅰ
the construction, and other general results
1.markov processes and their semigroups
2.semigroups and their generators
3.the construction of generators for particle systems
4.applications of the construction
5.the martingale problem
6.the martingale problem for particle systems
7.examples
8.notes and references
9.open problems
chapter ⅱ
some basic tools
1.coupling
2.monotonicity and positive correlations
3.duality
4.relative entropy
5.reversibility
6.recurrence and transience of reversible markov chains
7.superpositions of commuting markov chains
8.perturbations of random walks
9.notes and references
chapter ⅲ
spin systems
1.couplings for spin systems
2.attractive spin systems
3.attractive nearest-neighbor spin systems on z1
4.duality for spin systems
5.applications of duality
6.additive spin systems and the graphical representation
7.notes and references
8.open problems
chapter ⅳ
stochastic ising models
1.gibbs states
2.reversibility of stochastic ising models
3.phase transition
4.l2 theory
5.characterization of invariant measures
6.notes and references
7.open problems
chapter ⅴ
the voter model
1.ergodic theorems
2.properties of the invariant measures
3.clustering in one dimension
4.the finite system
5.notes and references
chapter ⅵ
the contact process
1.the critical value
2.convergence theorems
3.rates of convergence
4.higher dimensions
5.notes and references
6.open problems
chapter ⅶ
nearest-particle systems
1.reversible finite systems
2.general finite systems
3.construction of infinite systems
4.reversible infinite systems
5.general infinite systems
6.notes and references
7.open problems
chapter ⅷ
the exclusion process
1.ergodic theorems for symmetric systems
2.coupling and invariant measures for general systems
3.ergodic theorems for translation invariant systems
4.the tagged particle process
5.nonequilibrium behavior
6.notes and references
7.open problems
chapter ⅸ
linear systems with values in [0, oo）s
1.the construction; coupling and duality
2.survival and extinction
3.survival via second moments
4.extinction in one and two dimensions
5.extinction in higher dimensions
6.examples and applications
7.notes and references
8.open problems
bibliography
index
postface
errata
相互作用粒子系统 节选
里戈特编著的《相互作用粒子系统》旨在为读者全新展示随机过程这门课程。在过去的十五年里这门课程有了更深入研究,文中的材料都是之前没有以书本的形式出现过的。有关这门科技含量很高的科目,这本高质量的教程使得该科目立刻生动起来,并且尽可能多的包含一些容易理解的开放问题。对于每一位学习随机课程的学生,本书都不容错过。目次:结构和其他一般结果;一些基本工具;自旋系统;随机Ising模型;投票模型;接触法;*近粒子系统;排除过程;值在[0,∞ ]s上的线性系统。读者对象:数学、金融、统计专业的本科生、研究生和相关的科研人员。
